How do you express #cos(4theta)# in terms of #cos(2theta)#?
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To express ( \cos(4\theta) ) in terms of ( \cos(2\theta) ), you can use the double angle identities for cosine:
[ \cos(2\theta) = 2\cos^2(\theta) - 1 ]
Using this identity, you can rewrite ( \cos(4\theta) ) in terms of ( \cos(2\theta) ) as follows:
[ \cos(4\theta) = \cos(2(2\theta)) ]
[ = 2\cos^2(2\theta) - 1 ]
[ = 2(2\cos^2(\theta) - 1)^2 - 1 ]
[ = 2(4\cos^4(\theta) - 4\cos^2(\theta) + 1) - 1 ]
[ = 8\cos^4(\theta) - 8\cos^2(\theta) + 1 ]
Therefore, ( \cos(4\theta) = 8\cos^4(\theta) - 8\cos^2(\theta) + 1 ) in terms of ( \cos(2\theta) ).
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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